Work intergration

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tuongdang

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A fuel oil tank is an upright cylinder, buried so that its circular top is 10ft10ft beneath ground level. The tank has a radius of 8ft and is 24ft high, although the current oil level is only 22ft deep. Calculate the work required to pump all of the oil to the surface. Oil weighs 50lb/ft3.
 
tuongdang said:
A fuel oil tank is an upright cylinder, buried so that its circular top is 10ft beneath ground level. The tank has a radius of 8ft and is 24ft high, although the current oil level is only 22ft deep. Calculate the work required to pump all of the oil to the surface. Oil weighs 50lb/ft3.
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Please share your work/thoughts about this assignment.

I would start this problem with a sketch of vertical cylinder. From the ground,

the top-oil level would be - how far down in the beginning (t = 0)?​
​
the bottom-oil level would be - how far down in the beginning (t = 0)?​
​
What is the total volume of the oil that needs to be pumped up?​
 
I've set up this equation:
integral from 0 to 22 with the inside: 64 pi dy (50) (24-y)
 
is it right?
 

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Based on your diagram is the top of the cylinder really 10 ft below the ground??
Why in your diagram does part of the 10 ft go below the bottom of the tank? What part of the 10 ft goes below the tank? Should that matter?
 
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